Does work here.
*http://www.bbc.co.uk/radio/player/bbc_radio_three
Your system details list shows an old Shockwave Flash 10.0 r32 plugin that may not work with the BBC side.<br />
It does work with the latest Flash player for Firefox 3.6.x and that is Flash 10.3 r183.
The Firefox 3.6.24 version that you currently run is no longer supported with security updates
You should update the Firefox 15.0.1 and install the latest Flash player.
You can find the latest Firefox release in all languages and for all Operating Systems here:
*Firefox 15.0.x: http://www.mozilla.org/en-US/firefox/all.html
*http://www.adobe.com/software/flash/about/
*http://helpx.adobe.com/flash-player.html